JEE Mains · Maths · STD 11 - 7. binomial theoram
If \(\sum_{r=0}^5 \frac{{ }^{11} C_{2r+1}}{2 r+2}=\frac{\mathrm{m}}{\mathrm{n}}, \operatorname{gcd}(\mathrm{m}, \mathrm{n})=1\), then \(\mathrm{m}-\mathrm{n}\) is equal to _______
- A 2001
- B 2004
- C 2035
- D 2040
Answer & Solution
Correct Answer
(C) 2035
Step-by-step Solution
Detailed explanation
\((1+x)^{11}={ }^{11} C_0+{ }^{11} C_1 x+{ }^{11} C_2 x^2+\cdots+{ }^{11} C_{11} x^{11} \) \( \int_0^1(1+x)^{11} d x=\int_0^1\left({ }^{11} C_0+{ }^{11} C_1 x+{ }^{11} C_2 x^2+\cdots+{ }^{11} C_{11} x x^{11}\right) d x \)…
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